code: def _draw_contour(
      f,
      x,
      y=None,
      surface=False,
      fill=True,
      scale=True,
      shift=False,
      density=5,
      kernel=None,
  ):
      """draw a contour plot for a given 2D function 'f'
  
      x and y are arrays used to set up a 2D mesh grid
      if fill is True, color fill the contours
      if surface is True, plot the contours as a 3D projection
      if scale is provided, scale the intensity as 'z = log(4*z*scale+1)+2'
      if shift is provided, shift the intensity as 'z = z+shift' (useful for -z's)
      use density to adjust the number of contour lines
      if kernel is provided, apply kernel to x and y, as [xi',yi'] = kernel([xi,yi])
      Using a kernel is very slow, as it calcuates inverse transform at each point
      """
      import numpy
      from matplotlib import cm
  
      if y is None:
          y = x
      x, y = numpy.meshgrid(x, y)
  
      if kernel:
          xy = numpy.array([x, y])
          xy_ = numpy.zeros_like(xy)
          for i in range(xy.T.shape[0]):
              xy_.T[i] = [kernel(j)[:2] for j in xy.T[i]]
          del xy
          # x,y = xy_
          # x,y was meshgrid, but is 'skewed' due to kernel transform
          # create a new grid from min,max points
          x = numpy.linspace(xy_[0].min(), xy_[0].max(), xy_.shape[-1])
          y = numpy.linspace(xy_[1].min(), xy_[1].max(), xy_.shape[-2])
          x, y = numpy.meshgrid(x, y)
  
          from mystic.solvers import fmin
  
          def inverse(xi):  # XXX: too simple for all cases?
              cost = lambda kx: numpy.abs(
                  numpy.array(kernel(kx)) - xi
              ).sum()
              return fmin(cost, xi, ftol=1e-2, disp=0, maxiter=20)
  
          k = inverse
      else:
          k = lambda xi: xi
  
      z = 0 * x
      s, t = x.shape
      for i in range(s):
          for j in range(t):
              xx, yy = x[i, j], y[i, j]
              z[i, j] = f(
                  k([xx, yy])
              )  # FIXME: VERY SLOW: solve x = k(x'), then f(x)
      if shift:
          if shift is True:
              shift = max(-numpy.min(z), 0.0) + 0.5  # exact minimum
          z = z + shift
      if scale:
          z = numpy.log(4 * z * scale + 1) + 2
      # XXX: need to 'correct' the z-axis (or provide easy conversion)
  
      import matplotlib.pyplot as plt
      from mpl_toolkits.mplot3d import axes3d
  
      fig = plt.figure()
      if (
          surface and fill is None
      ):  # 'hidden' option; full 3D surface plot
          ax = fig.axes[0] if fig.axes else plt.axes(projection="3d")
          d = max(11 - density, 1)  # or 1/density ?
          kwds = {
              "rstride": d,
              "cstride": d,
              "cmap": cm.jet,
              "linewidth": 0,
          }
          ax.plot_surface(x, y, z, **kwds)
      else:
          if surface:
              kwds = {"projection": "3d"}  # 3D
          elif surface is None:  # 1D
              raise NotImplementedError(
                  "need to add an option string parser"
              )
          else:
              kwds = {}  # 2D
          ax = fig.axes[0] if fig.axes else plt.axes(**kwds)
          density = 10 * density
          if fill:
              plotf = ax.contourf  # filled contours
          else:
              plotf = ax.contour  # wire contours
          plotf(x, y, z, density, cmap=cm.jet)
      return fig
  
imports: from collections.abc import Callable
label_desc: Use image node_id 25 for calling a global function with example usage: _draw_contour(f, x, y, surface, fill, scale, shift, density, kernel) and returns: fig, fmin